On Sat, May 15, 2010 at 2:28 PM, Max Cantor
Where is my bind statement doing a case analysis? Isn't it just propagating, in a sense, the case analysis that came from values coming into the monad via return or via throwError?
What you did was reimplement the Either -type- not the Either -monad-. To see this lets make a complete interface to Either and provide the two implementations of that, now, abstract data type. Every function using Either can be written using the following interface: class EitherLike e where injLeft :: a -> e a b injRight :: b -> e a b either :: (a -> c) -> (b -> c) -> e a b -> c And here are two implementations: instance EitherLike Either where injLeft = Left injRight = Right either = Prelude.either type CEEither a b = forall c. (a -> c) -> (b -> c) -> c instance EitherLike CEEither where injLeft a = \l r -> l a injRight b = \l r -> r b either f g e = e f g Now we can write your functions and the "standard" Either monad definitions in terms of this abstract interface.
retErrCPS :: a -> ErrCPS e m a retErrCPS x = ErrCPS $ \_ good -> good x
return x = Right x retEither x = injRight x retErrCPS x = ErrCPS $ injRight x
bindErrCPS :: ErrCPS e m b -> (b -> ErrCPS e m a) -> ErrCPS e m a bindErrCPS m f = ErrCPS $ \err good -> runErrCPS m err $ \x -> runErrCPS (f x) err good
bindErrCPS m f = ErrCPS $ either injLeft (runErrCPS . f) (runErrCPS m) Left e >>= _ = Left e Right a >>= f = f a bindEither m f = either injLeft f m So, modulo wrapping and unwrapping, the code is identical. In version of GHC prior to pointer tagging, a case analysis on Either would be implemented very much like the Church-encoded eliminator, i.e. in case e of Left a -> f a, Right b -> g b pre-pointer tagging GHC would push (essentially) f and g on a stack and enter e, e would then choose which of f or g to return to. So your representation is still doing a case analysis, it is just representing it a different way.
Also, why wouldn't callCC work here? I'm not that familiar with the ContT monad so any more details would be very much appreciated.
It's hard to implement a "global" abort with callCC. You can implement a local one easily by using an outer callCC to provide an "escape" continuation, but you have to explicitly pass around this "escape" continuation.